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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Metric characterizations of dimension for separable metric spaces

Authors: Ludvik Janos and Harold Martin
Journal: Proc. Amer. Math. Soc. 70 (1978), 209-212
MSC: Primary 54F45
MathSciNet review: 0474229
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Abstract: A subset B of a metric space (X, d) is called a d-bisector set iff there are distinct points x and y in X with $ B = \{ z:d(x,z) = d(y,z)\} $. It is shown that if X is a separable metrizable space, then $ \dim (X) \leqslant n$ iff X has an admissible metric d for which $ \dim (B) \leqslant n - 1$ whenever B is a d-bisector set. For separable metrizable spaces, another characterization of n-dimensionality is given as well as a metric dependent characterization of zero dimensionality.

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Keywords: Bisector set, star rigid metric, strongly rigid metric
Article copyright: © Copyright 1978 American Mathematical Society

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